A Closed-Form Parametrization and an Alternative Computational Algorithm for Approximating Slices of Minkowski Sums of Ellipsoids in R3

The current work aims to develop an approximation of the slice a Minkowski sum finite number ellipsoids, sliced up by arbitrarily oriented plane in Euclidean space R3 that, best author’s knowledge, has not been addressed yet. This actual is closed form explicit parametric equation case that passing through zones surface with high curvatures, namely “corners”. An alternative computational algorithm introduced for cases slices corners, which family ellipsoidal inner and outer bounds used construct “narrow strip” sum. strip can narrow persistently few more constructing precisely coincide on also applicable aspect ratio ellipsoids. In line main goal, some approximations are discussed, including so-called “Kurzhanski’s” bounds, be formulate